In the figure, a wire loop of dimensions L = 40.6 cm and w = 27.7 cm lies in a m

Question

In the figure, a wire loop of dimensions L = 40.6 cm and w = 27.7 cm lies in a magnetic held. What are the (a) magnitude E and (d) direction (clockwise or counterclockwise-or "none*' if E = 0) of the emf induced in the loop if B^rightarrow = (5.80 times 10^-2 T/m)y^k ? What are (c) E and (d) the direction if B^rightarrow = (6.07 times 10^-2 T/s)t^K^cap? What are (e) E and (f) the direction if B^rightarrow = (8.34 times 10^-2 T/m-s)yt^K^cap? What are (g) E and (h) the direction if B^rightarrow = (3.07 times 10^-2 T/m middot s)xt J^cap ? What are (i) E and (j) the direction if B^rightarrow = (5.00 times 10^-2 T/m middot s)yt^i^cap ?

Explanation / Answer

To have an induced emf, the magnetic field must be perpendicular (or have a nonzero component perpendicular) to the coil, and must be changing with time.

part a )

B = 5.80 x 10^-2 y*k

dB/dt = 0

e = 0

part b )

none

part c )

e = -AdB/dt

A = 0.406 m * 0.277 m = 0.112462 m^2

dB/dt = 6.07 x 10^-2 T/s

e = -6.83 x 10^-3 V

|e| = 6.83 mV

part d )

clockwise

par e )

phi = 0.406 * 8.34 x 10^-2*t integral y*dy

y = 0.277 m

phi= 1.45 x 10^-3 t

e = dphi/dt

e = 1.45 x 10^-3 V = 1.45 mV

part f ) clockwise

part g )

phi = 0

e = 0

part h ) none

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